If you want to have an analogy along those lines, Apple is more like a Starbucks prohibiting coffee bean providers other than the ones it has agreements with from coming into Starbucks locations to sell their coffee beans.

IMO this isn't the correct take. Starbucks' stores are their own property and as long as they follow applicable laws regarding public accommodations, health and safety and the like they're free to run their stores however they want to. Where I live, we've got a plethora of Starbucks but we've also got Peet's and a whole bunch of small coffee roasters/shops that seem to be doing just fine. To me, Apple's App Store is the same way - it's Apple's property, run by Apple and branded by Apple. Everyone who develops for it knows the rules and (for the most part) follows them, because Apple makes sure you read the rules in multiple different places.

I'm not asking to be the mayor of the App Store, just the mayor of my own phone.